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Heat conduction equation

  • To: mathgroup at
  • Subject: [mg32848] Heat conduction equation
  • From: "Maurizio Tomasi" <zio_tom78 at>
  • Date: Fri, 15 Feb 2002 02:49:50 -0500 (EST)
  • Sender: owner-wri-mathgroup at

Hello to everybody.

I am trying to find a solution to the heat conduction equation (in one
dimension) by using the Fourier transform.  The equation has the
following form:

   d T                         d T
C ------ + q delta(x) - k rho ----- = 0
      2                        d t
   d x

and the Cauchy condition is

                  |            i omega t
 T (x=x1, t=0) =  | c (omega) e          d omega

(at some point x1 the temperature must have a pre-defined spectral
shape).  The Dirac delta in the equation represents a source of heat
placed at x=0.

Could somebody give me a reference or an hint about possible analytical
solutions of this equation (in terms of generalized functions)?  I
managed to solve it by ignoring the second or the third term, but now I
need a *general* solution.

Thanks in advance

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